Coding an LFO in C

Question

I want to know how I could implement a Low Frequency Oscilator on a simple synth I've coded in C. First in order to understand how to make this happen I would like just to modulate a sine wave by a sine LFO, and then I would adapt this to other oscilators and so on.

I tried adapting to adapt this LFO formula I found on my sine oscilator:

dLFOAmplitude * dHertz * (sin(w(dLFOHertz) * dTime

But I didn't found a correct way to do this. Here's my sinewave generator function:

static void build_sine_table(int16_t *data, int wave_length) {

    double phase_increment = (2.0f * pi) / (double)wave_length;
    double current_phase = 0;

    for(int i = 0; i < wave_length; i++) {
      int sample = (int) (sin(current_phase) * INT16_MAX);     
        data[i] = (int16_t)sample;
        current_phase += phase_increment;
    }
}

EDIT: I tried again to multiply my lfo signal with my oscilator. Each time I'm doing it I got no sound released. Same by divinding. When I sum up the two signal I got sound but no modulation. Here's what I tried in order to follow advices from the comment:

static void build_sine_table(int16_t *data, int wave_length) {

    double phase_increment = (2.0f * pi) / (double)wave_length;
    int lfo_phase = (2.0f * pi) / 20 / 44100;
    double lfo = 0;
    double current_phase = 0;

    for(int i = 0; i < wave_length; i++) {
      int sample = (int) (0.5 * sin(current_phase) * INT16_MAX + 0.5 * sin(lfo) * INT16_MAX);

        data[i] = (int16_t)sample;
        current_phase += phase_increment;
        lfo += lfo_phase;
    }
}

I tried many other thing, and the "best result" I got was a wave looking like this :

I've spent a lot of time trying to figure out a to make it work, and the more I looking into it, the less I'm confident to be able of coding it.

Answer 1

Thanks a lot to TehWan ! Well I'm not quite sure if I succeded into building a proper LFO, but at least I've got a wave modulation function with interesting sound. Check this out:

In order to achieve this I implemented a very small part of the code provided by TehWan and try different approach and got the best result with this code:

static void build_sine_table(int16_t *data, int wave_length) {

    const double LFO_FREQUENCY = 5; // LFO frequency [Hz]
    const double SAMPLE_RATE = 44100; // Sample rate [Hz]
    const double CONVERSION_FACTOR = 32768.0;
    double phase_increment = (2 * pi) / (double)wave_length;
    double current_phase = 0;  // Initial phase [rad]
    double dphase = ((2 * pi * LFO_FREQUENCY) / SAMPLE_RATE); // Phase rate of change [rad/sample]
    double lfo = 0;



    for(int i = 0; i < wave_length; i++) {

      (int)(sin(lfo) * INT16_MAX);
      int sample = (int)((sin(current_phase) * INT16_MAX));
      lfo += dphase;
      current_phase += phase_increment + (0.2 * lfo);

      data[i] =  (data[i] / CONVERSION_FACTOR) + (int16_t)sample;


}

If someone sees something wrong here I'm reading to correct it. Anyway for the time being I will consider this my "LFO".

EDIT: TehWan thank you once again, well I didn't used much your code but at least it did help find out how to change my function.